An inductor, a resistor of 10 , and a capacitor of 40 F are connected in series to an AC source operating at an angular frequency of 5000 rad s ⁻¹ . If the current and voltage in the circuit are in phase, what is the value of the inductance?

Step-by-step solution

For the current and voltage to be in phase, the circuit must be in a state of resonance. At resonance, the inductive reactance equals the capacitive reactance ( X_L = X_C ), which gives the resonant angular frequency as: = 1 LC Squaring both sides and rearranging for L gives: L = 1 ^2 C Substituting the given values: = 5000 rad s ⁻¹ C = 40 F = 40 10⁻⁶ F L = 1 (5000)^2 40 10⁻⁶ L = 1 25 10^6 40 10⁻⁶ L = 1 1000 H = 1 mH Answer: 1 mH